1. Write the following power series using the summation notation. [0+1/3 (x-4)+2

Answer 5: x is the radian angle. sin x for small angles can be represented by sin x = x - x^3/3!+x^5/5!- etc. Now you can get the answer

ID: 2859862 • Letter: 1

Question

1. Write the following power series using the summation notation.

[0+1/3 (x-4)+2/4 (x-4)^2+3/5 (x-4)^3+?]

2. Write the following Taylor series using the summation notation.

f(x)=e^x, a=ln2

3. Evaluate the series below and give its interval of convergence.

?_(n=0)^?, e^(-nx)

4.You can combine two (or more) convergent power series on the same interval I. Using the properties of the geometric

Geometric function

f(x)=(1/(1-x))= ?_(k=0)^?, x^(k) = [1+x+x^2+x^3+....] f(3x)=1/(1-3x)

5.The sine function is a Taylor series which can be expanded as below. Approximate Sin (?) using the Taylor expansion.

sin(x) =[x-((x^3)/3!)+((x^5)/5!)-((x^7)/7!)]

Answer 5:

x is the radian angle.
sin x for small angles can be represented by
sin x = x - x^3/3!+x^5/5!- etc. Now you can get the answer

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